Long volatility: buy call option, sell shares buy put option, buy shares. • Short
volatility: sell call option, buy shares .... Examples of trading strategies. • Think of
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Harcourt Quarterly Hedge Fund Presentation Paris, November 2004 Updated January 2005
Trading Market Volatility Marco Avellaneda Finance Concepts 49-51 Avenue Victor Hugo 75116 Paris
[email protected]
Volatility Trading in a Nutshell • Long volatility: buy call option, sell shares buy put option, buy shares • Short volatility: sell call option, buy shares sell put option, sell shares
Long Vol
Short Vol
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SP 500 June05 1125 Call Vol=16% 180 160
Theoretical Value
140 120 100 80 60 40 20 0 950
975
1000
1025
1050
1075
1100
1125
1150
1175
1200
1225
1250
1275
Index value
1-day P/L for Long Call/Short Stock (Constant volatility=16%) 50
40
30
20
10
0 950
975
1000
1025
1050
1075
1100
1125
1150
1175
1200
1225
1250
1275
-10
P/L ≈ θ ⋅ (n 2 − 1)
θ = daily time - decay , n =
percent index change expected daily volatility
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Assuming an implied volatility drop of 1% Vol=15% 50
40
30
20
10
0 950
975
1000
1025
1050
1075
1100
1125
1150
1175
1200
1225
1250
1275
-10
3.80 loss if stock does not move and volatility drops 1%
A closer look at the profit-loss due to a change in volatility 6 5 4 3 2 1 0 1075
1100
1125
1150
1175
-1 -2 -3 -4 -5
1% move in vol => 8% move in premium for a 6m ATM option
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Book-keeping: profit/loss from a delta-hedged option position (
)
P/L = θ ⋅ n 2 − 1 + V ⋅ dσ or 2 1 (dI ) P/L = Γ ⋅ 2 − σ 2 dt + V ⋅ dσ 2 I
Return Characteristics • Implied volatility is a market forecast of the future volatility of the underlying stock (level-dependent)
•
Long volatility positions gain when realized volatility (over the lifetime of the option) is higher than implied volatility at inception
•
Changes in implied volatility affect the MTM of the position
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S&P500 Implied and Realized Volatilities
Are current levels of volatility justified? • Market volatility is at a historical low • We believe that these levels of volatility are associated with the ``investment cycle’’ in equities • The crash of 2000-2002 diminished the public’s appetite for equities • The volatility environment resembles the early 1990’s (somewhat)
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01-Jun-90 26-Feb-91
11-May-93 02/02/1994 10/28/1994 07/26/1995 04/19/96 01/14/97 10/08/97
Unemployment
07/07/98 04/01/99 12/27/1999 9/20/2000 06/18/2001 20-Mar-2002 12-Dec09/10/2003
VIX: Jan 1986- May 2004
19-Nov-91 14-Aug-92
VIX: 30-day Implied Volatility index of S&P 100
1987 Crash: 160%
80
70
60
50
VIX: Jan-Nov 2004
Iraq handover
This year’s VIX
Madrid
06-Sep-89
40
09-Dec-88
30
23-Jun-87 17-Mar-88
20
0 02-Jan-86 26-Sep-86
10
24
22
20
18
16
14
12
10
1/ 2/ 20 04 1/ 16 /2 00 4 1/ 30 /2 00 4 2/ 13 /2 00 4 2/ 27 /2 00 4 3/ 12 /2 00 4 3/ 26 /2 00 4 4/ 9/ 20 04 4/ 23 /2 00 4 5/ 7/ 20 04 5/ 21 /2 00 4 6/ 4/ 20 04 6/ 18 /2 00 4 7/ 2/ 20 04 7/ 16 /2 00 4 7/ 30 /2 00 4 8/ 13 /2 00 4 8/ 27 /2 00 4 9/ 10 /2 00 4 9/ 24 /2 00 4 10 /8 /2 00 10 4 /2 2/ 20 04
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Can we forecast volatility? • Volatility cannot be predicted over long periods of time • Option markets in stocks and indices provide ``market forecasts’’ for periods ranging from 1 month to 1 year • Statistical models may be used to forecast volatility over short periods of time • Importance of taking into account ``exogenous news’’ and events, macro news
Equity Volatility Markets • 3000 optionable stocks in the U.S., 500 names have liquid options • Index options (SPX, OEX) and ETF options (QQQ) • In Europe, liquid markets in Eurostoxx50 and DAX index options • Moderate liquidity in single-name options in Europe • Asia: Nikkei and Kospi200 are very active
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Examples of trading strategies •
Think of volatility trading as trading in insurance premiums (against large moves in the underlying stock)
•
Analyze market in options as an ``insurance’’ market via normative models and build positions
•
Long-only strategies: always buy volatility to capitalize on market dislocations. Typically proposed as an insurance overlay to other investments
•
Long-short strategies: relative value approach. Capitalize on perceived mispricing of options. Originated from market-making activities in dealing rooms. Only recently adapted to assetmanagement
•
Macro strategies: invest across asset classes (equity, fx, fixed income, currencies)
Long-Only Strategies •
Strategies are natural hedges/overlays
•
Performed well before 2001
• Performed less well after 2001 due to drop in levels • P/L profile: many small losses (time decay), occasional large windfalls
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Long-Short Strategies • Vega-neutrality as hedge to changes in market volatility • Sell AND buy volatility (like insurance/reinsurance) • Adapted from dealing room (market-making) practice • Use correlation models for the underlying assets and their volatilities • Require strict control of exposure to single-name risk and market crash risk
Practical aspects of vol trading • Market structure: specialist system in the US, OTC in Europe • Electronic versus voice trading • Reduction in trading costs and improved access allows hedge funds to compete with B&Ds • Liquidity in single names and ETFs can be a problem • Technical infrastructure for trade processing, riskmanagement, models, etc
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Worst-case scenarios for volatility trading & remedies • Short volatility positions are such that underlying stock moves considerably and implied volatility goes up • Long volatility positions are such that stocks move moderately and volatility collapses • Limit exposure by asset • Limit sector exposure • Limit correlation exposure (dispersion trading)
Links between volatility trading and primary markets • Issuers of structured products (guaranteed principal with equity upside) are sellers of long term equity volatility and correlation • Convertible bond issuers are sellers of equity volatility • Institutional investors tend to be long converts and banks are short structured notes • Hedging these exposures creates flows in listed options (Eurostoxx50, Dow, S&P) and basket trades (dispersion) which connect long-term volatility markets with listed markets • Estimated exposure by issuers of structured products is EUR 200 MM per correlation point (RISK, May 2004)
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